Project Grant 2506807
- This $199,999 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on Ricci flow and Ricci solitons. The Principal Investigator aims to extend the surgical construction techniques developed by Perelman to continue Ricci flows through singularities, with the goal of uncovering new geometric and topological applications. The research project has two main components: 1) classifying ancient Ricci flows...
- This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides USD 100,000 to Rutgers, The State University to study the dynamics of cylindrical singularities in geometric flows and ancient solutions. The main objective is to understand the formation and behavior of singularities that develop in certain types of geometric equations, such as the Ricci flow and mean curvature flow, which are used to evolve geometric objects like...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,998 Project Grant to the Massachusetts Institute of Technology (MIT) under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research on singularities and rigidity in geometric evolution equations. The research focuses on geometric flows, which model the evolution of geometric objects like functions, surfaces, or Riemannian metrics over time using nonlinear generalizations of the classical...
- This $200,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) aims to advance the study of Einstein metrics and Ricci flows in 4-dimensional topology at the Massachusetts Institute of Technology (MIT). The project will focus on understanding and constructing 4-dimensional Einstein metrics and Ricci flows, particularly examining singularities such as orbifold singularities, cusp formation, and collapsing. This research...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $141,490 Project Grant to the University of California, Santa Cruz (UCSC) under the Mathematical and Physical Sciences program (CFDA 47.049). The project seeks to study the geometry and topology of spaces with Ricci curvature bounded below, including both smooth manifolds and singular spaces. Key focus areas include investigating the fundamental groups of complete and non-compact manifolds with non-negative Ricci...
- This Federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $199,999 to the University of Tennessee to conduct research on the structure and behavior of ancient solutions to Ricci and mean curvature type geometric flows. The project aims to enhance the field's impact by involving graduate students and fostering collaborations across disciplines and institutions. The research will focus on developing classification results...
- The National Science Foundation (NSF) awarded a $339,999 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to New York University (NYU) for research on geometric analysis and complex geometry. The award supports the principal investigator's work on studying geometric structures of complex manifolds, including Calabi-Yau manifolds, and investigating the nature of singularities that arise in Ricci flow - a geometric evolution equation. The research aims to enhance...
- This federal Project Grant award of $199,056.00 from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports research on nonlinear geometric flows and singularity analysis. The principal investigator and their team at Columbia University aim to study the singular behavior of partial differential equations related to physical phenomena like turbulence, black holes, cancer cell accumulation, and neural activity. The research will focus on understanding...
- This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $300,000 to Yale University to advance research on singularities in minimal submanifolds and geometric flows. The two-part project aims to leverage the theory of self-expanders for mean curvature flow to establish sharp lower bounds for densities of minimal cones, and to address the fundamental question of uniqueness of blow-up limits at...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to New York University (NYU) for the period of August 1, 2023 to July 31, 2026. The grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), focuses on two key areas: Studying geometric evolution equations, specifically mean curvature flow and Ricci flow, with a focus on different aspects of regularity. This research aims to address longstanding open problems at the...
This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $149,911 to Arizona State University (ASU) to conduct research on the mathematical analysis of noncompact and singular Ricci flows. Ricci flow is a geometric heat equation that can model diverse physical phenomena, and this project seeks to better understand the behavior of solutions in highly singular regions and extend the analytic theory of the equation. The research aims to classify noncompact shrinking solitons, study finite-time singularity formation, and localize unique continuation methods for geometric flows. The project includes an educational component to mentor and train graduate students. Work will be performed at ASU's campus in Tempe, Arizona over the award period from September 1, 2025 to August 31, 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $149.9k | 7/28/25 |